Limit to a gravitational field?

If two objects, let's say two pool balls (or giant balls of neutronium for that matter), are placed in a closed universe that contains no other matter or energy, at rest with one another, is there a distance at which they exert absolutely no gravitational pull on each other? Or will there be some sort of gravitational interaction, regardless of how small, that will slowly pull them together given enough time?

We have two theories which essentially agree on the outcome. Newton's Gravity and Einstein's Curved Spacetime.

If you had a closed Universe with two pool balls and no other matter, you would still have to worry about inertia. As such, there should be some critical value out in space where the force of attraction (due to Gravity or Spacetime Curvature) would not overcome inertial resistance to movement.

They will always exert a "gravitational pull" on each other - but it will not always influence the movement of the other. At least... that's what we know of these matters thus far.

If two objects, let's say two pool balls (or giant balls of neutronium for that matter), are placed in a closed universe that contains no other matter or energy, at rest with one another, is there a distance at which they exert absolutely no gravitational pull on each other? Or will there be some sort of gravitational interaction, regardless of how small, that will slowly pull them together given enough time?

Assuming time starts when the objects are placed a distance d apart, they would exert absoloutely no gravitational pull on each other until t=d/c.

----As such, there should be some critical value out in space where the force of attraction (due to Gravity or Spacetime Curvature) would not overcome inertial resistance to movement.-----

Surely there is no threshold value for a force to reach in order to accelerate an object. I would have thought that using the Newtonian idea of gravity the two objects would move towards each other. I know little of GR but my guess is that the answer is the same but i stand to be corrected in both cases.

Antenna Guy, just to get this straight, you're saying that there is no point at which a gravitational field dissapates completely? A spacetime curve, regardless of distance, will stretch across the universe given enough time for it to stretch at C? Assuming an infinite, unbounded universe, wouldn't that imply some sort of infinite gravitational energy of some sort? Correct me please...

Apologies - poor choice of words on my part. By 'closed' I simply meant 'closed off to any external influence' including we the observer, not 'bounded'.

It seems to me that if a force can exert itself, no matter how small, over an infinite area, that it would translate as an infinite exertion of energy. But as I said before, that is (faulty) intuition, and I would appreciate being educated as to the reality of the situation.

Oh, and by spacetime curve I refer to the warping in spacetime caused by mass. Is there a far away enough point where the 'depression' would end and spacetime would be 'flat' again, as if the objects didn't exist at all as far as spacetime was concerned?

Oh, and by spacetime curve I refer to the warping in spacetime caused by mass. Is there a far away enough point where the 'depression' would end and spacetime would be 'flat' again, as if the objects didn't exist at all as far as spacetime was concerned?

I tell you what: You describe how you think gravitational effects follow "a spacetime curve", and we'll take it from there.

I'm subscribing to the high-school textbook model of a ball placed on a sheet of rubber which causes a curvature or depression in the sheet, aka spacetime.

Have you considered how long it takes for the ball to make that depression? If the ball is removed, does the depression vanish instantaneously?

Gravitational effects do not magically appear throughout space - they require a finite amount of time to propagate over finite distances. Infinite distances imply infinite time for effects to manifest themselves.

We have two theories which essentially agree on the outcome. Newton's Gravity and Einstein's Curved Spacetime.

If you had a closed Universe with two pool balls and no other matter, you would still have to worry about inertia. As such, there should be some critical value out in space where the force of attraction (due to Gravity or Spacetime Curvature) would not overcome inertial resistance to movement.

They will always exert a "gravitational pull" on each other - but it will not always influence the movement of the other. At least... that's what we know of these matters thus far.

Did you really mean to say this? If ball A has mass (inertial resistance) M and ball B attracts it with a force (gravitational pull) F then ball B will change ball A's acceleration by F/M. No matter how small F is, as long as there is gravitational pull, it will affect the movement.

If two objects, let's say two pool balls (or giant balls of neutronium for that matter), are placed in a closed universe that contains no other matter or energy, at rest with one another, is there a distance at which they exert absolutely no gravitational pull on each other? Or will there be some sort of gravitational interaction, regardless of how small, that will slowly pull them together given enough time?

According to theory (both Newtonian and general relativity) there is no distance limit to gravity, it goes on forever. However it does get less and less, and eventually it will be so weak you couldn't measure it. Indeed quantum theory says (in a horribly gross oversimplification) that very tiny values can't be reliably measured at all.

The other thing to bear in mind is that the universe is expanding, so at very large distances the expansion overtakes gravitational attraction and the masses would move apart. Indeed it is now believed that the expansion is accelerating. To put it crudely, as well as gravitational attraction related to mass, it is thought there is also a very weak repulsion independent of mass (so weak that it's noticeable only on very large galactic scales). (For technical descriptions see cosmic inflation and the cosmological constant.)

Then we are back where we started. The two objects would exert absoloutely no gravitational pull on each other until t=d/c.

I think this is irrelevant to what's being asked. You're assuming that two masses magically appear out of nowhere, contrary to all known laws of classical physics.

Hi DrGreg,

If you are arguing that continuity of time must hold, then let's say the initial condition of rest implies that the objects would be closer at either increasing, or decreasing time. In a relativistic context, one can assume that the strength of the gravitational field at either object would not reach a minima until after the objects had reached their maximum separation (the initial condition of rest).

I think time delay is relevant to how/where the problem was presented, and I chose to highlight it within the context of the problem.